Trait Float

pub trait Float: Sized {
    // Required methods
    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn trunc(self) -> Self;
    fn fract(self) -> Self;
    fn abs(self) -> Self;
    fn signum(self) -> Self;
    fn copysign(self, y: Self) -> Self;
    fn mul_add(self, a: Self, b: Self) -> Self;
    fn div_euc(self, rhs: Self) -> Self;
    fn mod_euc(self, rhs: Self) -> Self;
    fn powi(self, n: i32) -> Self;
    fn powf(self, n: Self) -> Self;
    fn sqrt(self) -> Self;
    fn exp(self) -> Self;
    fn exp2(self) -> Self;
    fn ln(self) -> Self;
    fn log(self, base: Self) -> Self;
    fn log2(self) -> Self;
    fn log10(self) -> Self;
    fn abs_sub(self, other: Self) -> Self;
    fn cbrt(self) -> Self;
    fn hypot(self, other: Self) -> Self;
    fn sin(self) -> Self;
    fn cos(self) -> Self;
    fn tan(self) -> Self;
    fn asin(self) -> Self;
    fn acos(self) -> Self;
    fn atan(self) -> Self;
    fn atan2(self, other: Self) -> Self;
    fn sin_cos(self) -> (Self, Self)
       where Self: Sized;
    fn exp_m1(self) -> Self;
    fn ln_1p(self) -> Self;
    fn sinh(self) -> Self;
    fn cosh(self) -> Self;
    fn tanh(self) -> Self;
    fn asinh(self) -> Self;
    fn acosh(self) -> Self;
    fn atanh(self) -> Self;
}

Copy and pasted from Rust std

Required Methods

fn floor(self) -> Self

Returns the largest integer less than or equal to a number.

Examples

let f = 3.99_f64;
let g = 3.0_f64;

assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);

fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number.

Examples

let f = 3.01_f64;
let g = 4.0_f64;

assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);

fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0.

Examples

let f = 3.3_f64;
let g = -3.3_f64;

assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);

fn trunc(self) -> Self

Returns the integer part of a number.

Examples

let f = 3.3_f64;
let g = -3.7_f64;

assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), -3.0);

fn fract(self) -> Self

Returns the fractional part of a number.

Examples

let x = 3.5_f64;
let y = -3.5_f64;
let abs_difference_x = (x.fract() - 0.5).abs();
let abs_difference_y = (y.fract() - (-0.5)).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

fn abs(self) -> Self

Computes the absolute value of self. Returns NAN if the number is NAN.

Examples

use std::f64;

let x = 3.5_f64;
let y = -3.5_f64;

let abs_difference_x = (x.abs() - x).abs();
let abs_difference_y = (y.abs() - (-y)).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

assert!(f64::NAN.abs().is_nan());

fn signum(self) -> Self

Returns a number that represents the sign of self.

• 1.0 if the number is positive, +0.0 or INFINITY
• -1.0 if the number is negative, -0.0 or NEG_INFINITY
• NAN if the number is NAN

Examples

use std::f64;

let f = 3.5_f64;

assert_eq!(f.signum(), 1.0);
assert_eq!(f64::NEG_INFINITY.signum(), -1.0);

assert!(f64::NAN.signum().is_nan());

fn copysign(self, y: Self) -> Self

Returns a number composed of the magnitude of self and the sign of y.

Equal to self if the sign of self and y are the same, otherwise equal to -self. If self is a NAN, then a NAN with the sign of y is returned.

Examples

#![feature(copysign)]
use std::f64;

let f = 3.5_f64;

assert_eq!(f.copysign(0.42), 3.5_f64);
assert_eq!(f.copysign(-0.42), -3.5_f64);
assert_eq!((-f).copysign(0.42), 3.5_f64);
assert_eq!((-f).copysign(-0.42), -3.5_f64);

assert!(f64::NAN.copysign(1.0).is_nan());

fn mul_add(self, a: Self, b: Self) -> Self

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an unfused multiply-add.

Using mul_add can be more performant than an unfused multiply-add if the target architecture has a dedicated fma CPU instruction.

Examples

let m = 10.0_f64;
let x = 4.0_f64;
let b = 60.0_f64;

// 100.0
let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();

assert!(abs_difference < 1e-10);

fn div_euc(self, rhs: Self) -> Self

Calculates Euclidean division, the matching method for mod_euc.

This computes the integer n such that self = n * rhs + self.mod_euc(rhs). In other words, the result is self / rhs rounded to the integer n such that self >= n * rhs.

Examples

#![feature(euclidean_division)]
let a: f64 = 7.0;
let b = 4.0;
assert_eq!(a.div_euc(b), 1.0); // 7.0 > 4.0 * 1.0
assert_eq!((-a).div_euc(b), -2.0); // -7.0 >= 4.0 * -2.0
assert_eq!(a.div_euc(-b), -1.0); // 7.0 >= -4.0 * -1.0
assert_eq!((-a).div_euc(-b), 2.0); // -7.0 >= -4.0 * 2.0

fn mod_euc(self, rhs: Self) -> Self

Calculates the Euclidean modulo (self mod rhs), which is never negative.

In particular, the return value r satisfies 0.0 <= r < rhs.abs() in most cases. However, due to a floating point round-off error it can result in r == rhs.abs(), violating the mathematical definition, if self is much smaller than rhs.abs() in magnitude and self < 0.0. This result is not an element of the function’s codomain, but it is the closest floating point number in the real numbers and thus fulfills the property self == self.div_euc(rhs) * rhs + self.mod_euc(rhs) approximatively.

Examples

#![feature(euclidean_division)]
let a: f64 = 7.0;
let b = 4.0;
assert_eq!(a.mod_euc(b), 3.0);
assert_eq!((-a).mod_euc(b), 1.0);
assert_eq!(a.mod_euc(-b), 3.0);
assert_eq!((-a).mod_euc(-b), 1.0);
// limitation due to round-off error
assert_ne!((-std::f64::EPSILON).mod_euc(3.0), 0.0);

fn powi(self, n: i32) -> Self

Raises a number to an integer power.

Using this function is generally faster than using powf

Examples

let x = 2.0_f64;
let abs_difference = (x.powi(2) - x*x).abs();

assert!(abs_difference < 1e-10);

fn powf(self, n: Self) -> Self

Raises a number to a floating point power.

Examples

let x = 2.0_f64;
let abs_difference = (x.powf(2.0) - x*x).abs();

assert!(abs_difference < 1e-10);

fn sqrt(self) -> Self

Takes the square root of a number.

Returns NaN if self is a negative number.

Examples

let positive = 4.0_f64;
let negative = -4.0_f64;

let abs_difference = (positive.sqrt() - 2.0).abs();

assert!(abs_difference < 1e-10);
assert!(negative.sqrt().is_nan());

fn exp(self) -> Self

Returns e^(self), (the exponential function).

Examples

let one = 1.0_f64;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn exp2(self) -> Self

Returns 2^(self).

Examples

let f = 2.0_f64;

// 2^2 - 4 == 0
let abs_difference = (f.exp2() - 4.0).abs();

assert!(abs_difference < 1e-10);

fn ln(self) -> Self

Returns the natural logarithm of the number.

Examples

let one = 1.0_f64;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn log(self, base: Self) -> Self

Returns the logarithm of the number with respect to an arbitrary base.

The result may not be correctly rounded owing to implementation details; self.log2() can produce more accurate results for base 2, and self.log10() can produce more accurate results for base 10.

Examples

let five = 5.0_f64;

// log5(5) - 1 == 0
let abs_difference = (five.log(5.0) - 1.0).abs();

assert!(abs_difference < 1e-10);

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

Examples

let two = 2.0_f64;

// log2(2) - 1 == 0
let abs_difference = (two.log2() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

Examples

let ten = 10.0_f64;

// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn abs_sub(self, other: Self) -> Self

👎Deprecated: you probably meant (self - other).abs(): this operation is (self - other).max(0.0) (also known as fdim in C). If you truly need the positive difference, consider using that expression or the C function fdim, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).

The positive difference of two numbers.

• If self <= other: 0:0
• Else: self - other

Examples

let x = 3.0_f64;
let y = -3.0_f64;

let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

fn cbrt(self) -> Self

Takes the cubic root of a number.

Examples

let x = 8.0_f64;

// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();

assert!(abs_difference < 1e-10);

fn hypot(self, other: Self) -> Self

Calculates the length of the hypotenuse of a right-angle triangle given legs of length x and y.

Examples

let x = 2.0_f64;
let y = 3.0_f64;

// sqrt(x^2 + y^2)
let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();

assert!(abs_difference < 1e-10);

fn sin(self) -> Self

Computes the sine of a number (in radians).

Examples

use std::f64;

let x = f64::consts::PI/2.0;

let abs_difference = (x.sin() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn cos(self) -> Self

Computes the cosine of a number (in radians).

Examples

use std::f64;

let x = 2.0*f64::consts::PI;

let abs_difference = (x.cos() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn tan(self) -> Self

Computes the tangent of a number (in radians).

Examples

use std::f64;

let x = f64::consts::PI/4.0;
let abs_difference = (x.tan() - 1.0).abs();

assert!(abs_difference < 1e-14);

fn asin(self) -> Self

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1].

Examples

use std::f64;

let f = f64::consts::PI / 2.0;

// asin(sin(pi/2))
let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();

assert!(abs_difference < 1e-10);

fn acos(self) -> Self

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1].

Examples

use std::f64;

let f = f64::consts::PI / 4.0;

// acos(cos(pi/4))
let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();

assert!(abs_difference < 1e-10);

fn atan(self) -> Self

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

Examples

let f = 1.0_f64;

// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn atan2(self, other: Self) -> Self

Computes the four quadrant arctangent of self (y) and other (x) in radians.

• x = 0, y = 0: 0
• x >= 0: arctan(y/x) -> [-pi/2, pi/2]
• y >= 0: arctan(y/x) + pi -> (pi/2, pi]
• y < 0: arctan(y/x) - pi -> (-pi, -pi/2)

Examples

use std::f64;

let pi = f64::consts::PI;
// Positive angles measured counter-clockwise
// from positive x axis
// -pi/4 radians (45 deg clockwise)
let x1 = 3.0_f64;
let y1 = -3.0_f64;

// 3pi/4 radians (135 deg counter-clockwise)
let x2 = -3.0_f64;
let y2 = 3.0_f64;

let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();

assert!(abs_difference_1 < 1e-10);
assert!(abs_difference_2 < 1e-10);

fn sin_cos(self) -> (Self, Self)

where Self: Sized,

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

Examples

use std::f64;

let x = f64::consts::PI/4.0;
let f = x.sin_cos();

let abs_difference_0 = (f.0 - x.sin()).abs();
let abs_difference_1 = (f.1 - x.cos()).abs();

assert!(abs_difference_0 < 1e-10);
assert!(abs_difference_1 < 1e-10);

fn exp_m1(self) -> Self

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

Examples

let x = 7.0_f64;

// e^(ln(7)) - 1
let abs_difference = (x.ln().exp_m1() - 6.0).abs();

assert!(abs_difference < 1e-10);

fn ln_1p(self) -> Self

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

Examples

use std::f64;

let x = f64::consts::E - 1.0;

// ln(1 + (e - 1)) == ln(e) == 1
let abs_difference = (x.ln_1p() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn sinh(self) -> Self

Hyperbolic sine function.

Examples

use std::f64;

let e = f64::consts::E;
let x = 1.0_f64;

let f = x.sinh();
// Solving sinh() at 1 gives `(e^2-1)/(2e)`
let g = (e*e - 1.0)/(2.0*e);
let abs_difference = (f - g).abs();

assert!(abs_difference < 1e-10);

fn cosh(self) -> Self

Hyperbolic cosine function.

Examples

use std::f64;

let e = f64::consts::E;
let x = 1.0_f64;
let f = x.cosh();
// Solving cosh() at 1 gives this result
let g = (e*e + 1.0)/(2.0*e);
let abs_difference = (f - g).abs();

// Same result
assert!(abs_difference < 1.0e-10);

fn tanh(self) -> Self

Hyperbolic tangent function.

Examples

use std::f64;

let e = f64::consts::E;
let x = 1.0_f64;

let f = x.tanh();
// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
let abs_difference = (f - g).abs();

assert!(abs_difference < 1.0e-10);

fn asinh(self) -> Self

Inverse hyperbolic sine function.

Examples

let x = 1.0_f64;
let f = x.sinh().asinh();

let abs_difference = (f - x).abs();

assert!(abs_difference < 1.0e-10);

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

Examples

let x = 1.0_f64;
let f = x.cosh().acosh();

let abs_difference = (f - x).abs();

assert!(abs_difference < 1.0e-10);

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

Examples

use std::f64;

let e = f64::consts::E;
let f = e.tanh().atanh();

let abs_difference = (f - e).abs();

assert!(abs_difference < 1.0e-10);

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl Float for f32

fn floor(self) -> f32

fn ceil(self) -> f32

fn round(self) -> f32

fn trunc(self) -> f32

fn fract(self) -> f32

fn abs(self) -> f32

fn signum(self) -> f32

fn copysign(self, y: f32) -> f32

fn mul_add(self, a: f32, b: f32) -> f32

fn div_euc(self, rhs: f32) -> f32

fn mod_euc(self, rhs: f32) -> f32

fn powi(self, n: i32) -> f32

fn powf(self, n: f32) -> f32

fn sqrt(self) -> f32

fn exp(self) -> f32

fn exp2(self) -> f32

fn ln(self) -> f32

fn log(self, base: f32) -> f32

fn log2(self) -> f32

fn log10(self) -> f32

fn abs_sub(self, other: f32) -> f32

👎Deprecated: you probably meant (self - other).abs(): this operation is (self - other).max(0.0) (also known as fdim in C). If you truly need the positive difference, consider using that expression or the C function fdim, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).

fn cbrt(self) -> f32

fn hypot(self, other: f32) -> f32

fn sin(self) -> f32

fn cos(self) -> f32

fn tan(self) -> f32

fn asin(self) -> f32

fn acos(self) -> f32

fn atan(self) -> f32

fn atan2(self, other: f32) -> f32

fn sin_cos(self) -> (f32, f32)

fn exp_m1(self) -> f32

fn ln_1p(self) -> f32

fn sinh(self) -> f32

fn cosh(self) -> f32

fn tanh(self) -> f32

fn asinh(self) -> f32

fn acosh(self) -> f32

fn atanh(self) -> f32

impl Float for f64

fn floor(self) -> f64

fn ceil(self) -> f64

fn round(self) -> f64

fn trunc(self) -> f64

fn fract(self) -> f64

fn abs(self) -> f64

fn signum(self) -> f64

fn copysign(self, y: f64) -> f64

fn mul_add(self, a: f64, b: f64) -> f64

fn div_euc(self, rhs: f64) -> f64

fn mod_euc(self, rhs: f64) -> f64

fn powi(self, n: i32) -> f64

fn powf(self, n: f64) -> f64

fn sqrt(self) -> f64

fn exp(self) -> f64

fn exp2(self) -> f64

fn ln(self) -> f64

fn log(self, base: f64) -> f64

fn log2(self) -> f64

fn log10(self) -> f64

fn abs_sub(self, other: f64) -> f64

👎Deprecated: you probably meant (self - other).abs(): this operation is (self - other).max(0.0) (also known as fdim in C). If you truly need the positive difference, consider using that expression or the C function fdim, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).

fn cbrt(self) -> f64

fn hypot(self, other: f64) -> f64

fn sin(self) -> f64

fn cos(self) -> f64

fn tan(self) -> f64

fn asin(self) -> f64

fn acos(self) -> f64

fn atan(self) -> f64

fn atan2(self, other: f64) -> f64

fn sin_cos(self) -> (f64, f64)

fn exp_m1(self) -> f64

fn ln_1p(self) -> f64

fn sinh(self) -> f64

fn cosh(self) -> f64

fn tanh(self) -> f64

fn asinh(self) -> f64

fn acosh(self) -> f64

fn atanh(self) -> f64

Implementors